An interpretation of multiplier ideals via tight closure

2001/11/16 by Shunsuke Takagi, Takagi, Shunsuke · 6 citations
Computer Science · Mathematics · #13A35 #14B05 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Rings, Modules, and Algebras #math.AC #math.AG #msc:13A35 #msc:14B05

paper · pdf · doi:10.48550/arxiv.math/0111187

21 pages in AMS LaTeX, to appear in Journal of Algebraic Geometry

openalex publication_date 2001/11/16 · arxiv created 2002/11/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Hara and Smith independently proved that in a normal \mQ-Gorenstein ring of characteristic p ≫ 0, the test ideal coincides with the multiplier ideal associated to the trivial divisor. We extend this result for a pair (R, Δ) of a normal ring R and an effective \mQ-Weil divisor Δ on \Spec R. As a corollary, we obtain the equivalence of strongly F-regular pairs and klt pairs.

Cited by

• On the uniform positivity of F-signature under reduction modulo p
• On Grauert-Riemenschneider vanishing for Cohen-Macaulay schemes of klt type
• On volumes and the generic invariance of Fano type varieties
• Boundedness of complements for fibered Fano threefolds in positive characteristic
• Limit F -signature functions of two-variable binomial hypersurfaces
• Limit F-signature functions of two-variable binomial hypersurfaces

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